Channel entrance flow and its linear stability

Abstract

In this work, we present a temporal linear stability analysis of developing channel flow. For the main flow, the considered solution is analytic. It is based on the hypothesis of small disturbances from fully developed flow and it is valid for intermediate Reynolds numbers. The disturbances are separated into symmetric and anti-symmetric eigenmodes of the velocity. We deal subsequently with the linear stability of this main flow, taking into account the nearly parallel flow assumption. The stability problem formulation leads to the Orr–Sommerfeld equation. This equation is then resolved using the Chebyshev spectral collocation method. The stability results depend essentially on the shape and amplitude of the velocity profiles imposed at the channel entry.

Stability Analysis of Plane Couette-Poiseuille Flow With Porous Walls Under Transverse Magnetic Field

“…The spectrum is plotted in figure 1 (a). It is worth noting, from the results in this figure, that the curves converge in excellent agreement toward that obtained by Dongorra et al [23] when they used the Chebyshev tau-QZ algorithm method and Hifdi et al [24] and Rafiki et al [19] by the Chebyshev spectral collocation method. Moreover, the critical Reynolds and wave numbers are converging, respectively, to Rec = 5772.2210, αc = 1.0205 [22] for 60 collocation points [see figure 1 (b)].…”

DNS of bypass transition in entrance channel flow induced by boundary layer interaction

“…Biau et al [8] have also studied linear stability of the plane developping channel flow, adopting a basis flow characteristic of the far-downstream region and similar to the one used by Asai and Floryan [3]. Their modal analysis, conducted in the spatial framework with parallel-flow approximation, complements the temporal study made by Hifdi et al [32]. Optimal transient perturbations have also been determined using the parabolized equations.…”

Linear stability of channel entrance flow

“…In compact form this system can be noted as Lq n = α nqn . The modal stability, for arbitrary base flow distortion, was studied earlier by Hidfi et al [7]. The work of these authors has been conducted in the temporal framework, which is simpler but not as physically relevant as the spatial framework for the kind of open flows examined here.…”